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An Analysis of Two Interventions Designed to Improve Student Performance in Engineering Calculus

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2013 ASEE Annual Conference & Exposition


Atlanta, Georgia

Publication Date

June 23, 2013

Start Date

June 23, 2013

End Date

June 26, 2013



Conference Session

FPD 8: Engineering Math Issues

Tagged Division

First-Year Programs

Page Count


Page Numbers

23.148.1 - 23.148.12



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Paper Authors


Julia H. Chariker University of Louisville

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JULIA H. CHARIKER, Ph.D., is a postdoctoral scholar in the Department of Psychological and Brain Sciences and the Bioinformatics Core at the University of Louisville, Louisville, Kentucky. She teaches courses in human cognition and learning. Her research combines the psychology of learning and cognition, new information technologies, and collaboration with experts in biology, medicine, and engineering.

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Patricia A Ralston University of Louisville

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Patricia A. S. Ralston is Professor and Chair of the Department of Engineering Fundamentals. She received her B.S., MEng, and PhD degrees in chemical engineering from the University of Louisville. Her educational research interests include the use of technology in engineering education, incorporation of critical thinking in engineering education, and ways to improve retention. Her other interests include process modeling, simulation, and process control.

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Jeffrey Lloyd Hieb University of Louisville

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Jeffrey L. Hieb, Ph.D. is an Assistant Professor with the Department of Engineering Fundamentals. He teaches engineering mathematics to freshman and sophomore engineering students. His research interests include: computer security, cyber-security for industrial control systems, microkernel based operating systems and the use of technology in engineering education.

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Carrye Y Wilkins University of Louisville

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Carrye Wilkins received her undergraduate and graduate degree in mathematics from the University of Louisville. She is the Associate Director of Resources for Academic Achievement, REACH, at the University of Louisville where she serves as the coordinator of the Math Resource Center and math instructor in the Mathematics Department. In her role as coordinator, she manages the Math Resource Center, onsite and online Virtual Math Center, ADVANCE in Mathematics Program, SPEED Calculus Preview Program, and Math Seminars. For the past 19 years, some of her duties have included managing and creating support services for math students; hiring, training, and evaluating tutors and Graduate Student Assistants; and mentoring tutors and students. She has attended and presented material at numerous local and national conferences and has dedicated her time and effort to promoting the intellectual and personal growth of undergraduate students, regardless of their culture or skill level.

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An Analysis of Interventions Designed to Improve Retention of First Year Engineering Students The XXX School of Engineering is a large, urban, institution in the southeast. Historically, theSchool taught its own mathematics for engineering undergraduates, placing a high priority on a sequenceof calculus-based courses: Engineering Analysis I, II, and III. Retention of freshman engineering studentshas long been a goal of the school, more recently a goal specifically of the Engineering FundamentalsDepartment, which teaches all undergraduate engineering mathematics courses. It is well documented thatretention of engineering students is related to their first fall semester GPA and that performance in a firstmathematics course has a large impact on the first fall GPA [1]. Furthermore, it is also documented thatentry-level calculus continues to be a challenge for many engineering students [2, 3, 4, 5]. A long standing effort to help entering freshman who struggle with Engineering Analysis I hasbeen the offering of Introduction to Calculus to freshman who have performed poorly on the first twoexams in Engineering Analysis I. Introduction to Calculus gives struggling students the opportunity tomaintain a high GPA while they review algebra, trigonometry, functions, and basic calculus concepts at aslower pace. Placement tests and other assessments to determine students’ readiness for EngineeringAnalysis I have been previously explored, but no quantifiable results were reached. Offering this coursehas prevented many D, F, and W grades in Engineering Analysis I the first fall semester, but thedepartment is continuing to seek approaches that both decrease the number of students needing thiscourse, and improve the performance of those students who to take taking Introduction to Calculus. Oneof these approaches, added within the last five years, is a summer calculus preview program whichreviews algebra. To determine which students to target for the summer program, an algebra readiness exam (ARE)was developed by faculty and offered to incoming students during orientation. The ARE was intended toidentify students in need of algebra review prior to starting Engineering Analysis I, and the summerprogram was intended to provide the needed review. Students who scored below 80% on the ARE wereencouraged to take the preview program, though neither the ARE nor the preview program were required.During the first two years of the program the number of students taking the ARE and the previewprogram was low. However, there was some indication that the program was having a positive impact forthose who participated. To encourage more students to take advantage of the program, in 2011 the AREbecame a requirement for Engineering Analysis I, counting 5% of the final grade. Nearly the entire freshman class took the ARE in 2011 (340 students). Analysis of the scoresfrom the 2011 cohort of Engineering Analysis I students found that ARE scores were positively related tomean exam performance and mean quiz performance in Engineering Analysis I (see Figure 1). The AREwas also a significant predictor of retention in Engineering Analysis I, as ARE scores increased, studentswere more likely to remain in Engineering Analysis I. Furthermore, students who participated in thesummer intervention program were also more likely to remain in Engineering Analysis I. Although AREscores of students participating in the summer intervention were lower than the scores of students who didnot participate, students completing the summer intervention performed similarly on exams and quizzes inEngineering Analysis I. The analysis seems to indicate that there are some freshmen who are at risk of struggling inEngineering Analysis I due to algebra deficiencies but who are able to perform at the same level as theirpeers who did not have algebra deficiencies after only a summer intervention. Due to self-selection theremay be other factors contributing to the improvement. There is clearly a second group of freshmen thatneed the semester long remediation offered by Introduction to Calculus. Given our findings, it should bepossible to use the ARE to identify students, prior to the beginning of the semester, who would be mostlikely to benefit from participating in the summer intervention. The department intends to use thisanalysis to increase the participation in the summer intervention program, knowing that this will likelylead to improved retention in Engineering Analysis I. 100 100 90 90 80 80Mean Exam Performance Mean Quiz Performance 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Algebra Readiness Exam Algebra Readiness ExamFigure 2. Mean exam performance (left) and mean quiz performance (right) in Engineering Analysis I as a function of Algebra Readiness scores. A regression line is presented in blue. Circles represent individual student data.Reference[1] Budny, D., LeBold, W., and Bjedov, G., “Assessment of the Impact of Freshman EngineeringCourses”, Journal of Engineering Education, October 1998, pp.405-411.[2] Habre, S. and Abboud, M., “Students’Conceptual Understanding of a Function and itsDerivative in an Experimental Calculus Course”, Journal of Mathematics Behavior, Vol. 25,2006, pp. 57-72.[3] Judson, T. and Nishimori, T., “Concepts and Skills in High School Calculus: An Examinationof a Special Case in Japan and the United States”, Journal for Research in MathematicsEducation, Vol. 36 (1), 2005, pp. 24-43.[4] Moore, J., “Undergraduate Mathematics Achievement in Emerging Ethnic EngineersProgramme”, International Journal of Mathematical Education in Science and Technology, Vol.36 (5), 2005, pp. 529-537.[5] Subramaniam, P., Cates, M., and Borislava, G., “Improving Success Rates in Calculus”, MAAFocus Vol. 28 (5), 2008, pp. 20-21

Chariker, J. H., & Ralston, P. A., & Hieb, J. L., & Wilkins, C. Y. (2013, June), An Analysis of Two Interventions Designed to Improve Student Performance in Engineering Calculus Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--19162

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